A classification of locally semicomplete digraphs

Recently, Huang (1995) gave a characterization of local tournaments. His characterization involves arc-reversals and therefore may not be easily used to solve other structural problems on locally semicomplete digraphs (where one deals with a fixed locally semicomplete digraph). In this paper we derive a classification of locally semicomplete digraphs which is very useful for studying structural properties of locally semicomplete digraphs and which does not depend on Huang's characterization. An advantage of this new classification of locally semicomplete digraphs is that it allows one to prove results for locally semicomplete digraphs without reproving the same statement for tournaments. We use our result to characterize pancyclic and vertex pancyclic locally semicomplete digraphs and to show the existence of a polynomial algorithm to decide whether a given locally semicomplete digraph has a kernel

A graph theoretic proof of the complexity of colouring by a local tournament with at least two directed cycles

In this paper we give a graph theoretic proof of the fact that deciding whether a homomorphism exists to a fixed local tournament with at least two directed cycles is NP-complete. One of the main reasons for the graph theoretic proof is that it showcases all of the techniques that have been built up over the years in the study of the digraph homomorphism problem

A graph theoretic proof of the complexity of colouring by a local tournament with at least two directed cycles

In this paper we give a graph theoretic proof of the fact that deciding whether a homomorphism exists to a fixed local tournament with at least two directed cycles is NP-complete. One of the main reasons for the graph theoretic proof is that it showcases all of the techniques that have been built up over the years in the study of the digraph homomorphism problem

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum

Parameterized Enumeration of Neighbour Strings and Kemeny Aggregations

In this thesis, we consider approaches to enumeration problems in the parameterized complexity setting. We obtain competitive parameterized algorithms to enumerate all, as well as several of, the solutions for two related problems Neighbour String and Kemeny Rank Aggregation. In both problems, the goal is to find a solution that is as close as possible to a set of inputs (strings and total orders, respectively) according to some distance measure. We also introduce a notion of enumerative kernels for which there is a bijection between solutions to the original instance and solutions to the kernel, and provide such a kernel for Kemeny Rank Aggregation, improving a previous kernel for the problem. We demonstrate how several of the algorithms and notions discussed in this thesis are extensible to a group of parameterized problems, improving published results for some other problems